A point `O` inside a rectangle `A B C D` is joined to the vertices. Prove that the sum of the areas of a pair of opposite triangles so formed is equal to the sum of the areas of other pair of triangles.

A point O inside a rectangle A B C D is joined to the vertices. Prove that the sum of the areas of a pair of opposite triangles so formed is equal to the sum of the other pair of triangles. Given: A rectangle A B C D\ a n d\ O is a point inside it. O A ,\ O B ,\ O C\ a n d\ O D have been joined. To Prove: a r\ (A O D)+\ a r\ ( B O C)=\ a r\ ( A O B)+\ a r( C O D)

Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle.

If the sides of a quadrilateral touch a circle, prove that the sum of a pair of opposite sides is equal to the sum of the other pair.

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

Prove that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle

Prove that the sum of opposite pair of angles of a cyclic quadrilateral is 180^@

Equilateral triangles are drawn on the sides of a right triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

Equilateral triangles are drawn on the sides of a right triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

The perimeter of an isosceles triangle is 40 cm. The base is two-third of the sum of equal sides. Find the area of the triangle .

If the areas of two similar triangles are equal, prove that they are congruent.